KONRAD BAJER a1, ANDREW P. BASSOM a2andANDREW D. GILBERT a2 a1 Institute of Geophysics, Warsaw University, Poland a2 Department of Mathematical Sciences, University of Exeter, North Park Road, Exeter, Devon EX4 4QE, UK
A point vortex is introduced into a weak background vorticity gradient at finite Reynolds number. As the vortex spreads viscously so the background vorticity becomes wrapped around it, leading to enhanced diffusion of vorticity, but also giving a feedback on the vortex and causing it to move. This is investigated in the linear approximation, using a similarity solution for the advection of weak vorticity around the vortex, at finite and infinite Reynolds number. A logarithmic divergence in the far field requires the introduction of an outer length scale $L$ and asymptotic matching. In this way results are obtained for the motion of a vortex in a weak vorticity field modulated on the large scale $L$ and these are confirmed by means of numerical simulations.